Circular motion angular velocity

[Abhishekdas]

Circular motion...angular velocity...

Homework Statement

This is a general question i have...Lets say a particle is moving in a plane (in any arbitrary way may or maynot be following any equation)...Now we are told to find the angular velocity of the particle with respect to a reference point at some instant...lets say you have the velocity vector of the particle and the position vector of the particle with respect to the reference point(or simply the distance between them).

Homework Equations

The Attempt at a Solution

A technique i came across(which i guess is common) is to take the component of the velocity which is perpendicular to the line joining the point and the particle and then dividing it by the distance between them.

Now does this method comes from analogy with circular motion where v=rw? I am not totally convinced by this method and i don't understand this properly...So please help...

 

[tiny-tim]

Hi Abhishekdas!

A technique i came across(which i guess is common) is to take the component of the velocity which is perpendicular to the line joining the point and the particle and then dividing it by the distance between them.

Now does this method comes from analogy with circular motion where v=rw? I am not totally convinced by this method and i don't understand this properly...So please help...

Yes, that's fine …

angular velocity = angle per time,

and to find the angle you're only interested in the projection of the velocity on a circle, ie the component of the velocity perpendicular to the line joining the point and the particle …

so you find that projection (an arc of a circle), then divide by the radius to get the angle

 

[Abhishekdas]

Hey thanks tiny-tim... i think i am kind of getting it...
Is it like the actual velocity is the hypotenuse of a right angled triangle and the base ie the projection is approximated as the arc and then it iss arc = r*d(theta)...
Am i thinking correctly?

 

[tiny-tim]

Yes that's right …

component and projection are the same thing.

 

[Abhishekdas]

ya...Thanks...got it...